Efficient splitting algorithms for the Schrödinger eigenvalue problem
with perturbed harmonic oscillator potentials in higher dimensions are considered.
The separability of the Hamiltonian makes the problem suitable for ...[+]

Efficient splitting algorithms for the Schrödinger eigenvalue problem
with perturbed harmonic oscillator potentials in higher dimensions are considered.
The separability of the Hamiltonian makes the problem suitable for the application
of splitting methods. Using algebraic techniques, we show how to apply Fourier
spectral methods to propagate higher dimensional quantum harmonic oscillators,
thus retaining the near integrable structure and fast computability. This methods is
then used to solve the eigenvalue problem by imaginary time propagation. High
order fractional time steps of order greater than two necessarily have negative
steps and can not be used for this class of diffusive problems. However, the use
of fractional complex time steps with positive real parts does not negatively impact
on stability and only moderately increases the computational cost. We analyze the
performance of this class of schemes and propose new highly optimized sixth-order
schemes for near integrable systems which outperform the existing ones in most
cases.[-]